Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.

Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.

If the value is small (i.e., fits into an Int), the IS constructor is used. Otherwise IP and IN constructors are used to store a BigNat representing the positive or the negative value magnitude, respectively.

Invariant: IP and IN are used iff the value does not fit in IS.

Used to implement (+) for the Num typeclass. This gives the sum of two integers.

Example

>>> plusInteger 3 2
5

>>> (+) 3 2
5

Used to implement (-) for the Num typeclass. This gives the difference of two integers.

Example

>>> minusInteger 3 2
1

>>> (-) 3 2
1

Used to implement (*) for the Num typeclass. This gives the product of two integers.

Example

>>> timesInteger 3 2
6

>>> (*) 3 2
6

Used to implement negate for the Num typeclass. This changes the sign of whatever integer is passed into it.

Example

>>> negateInteger (-6)
6

>>> negate (-6)
6

Used to implement abs for the Num typeclass. This gives the absolute value of whatever integer is passed into it.

Example

>>> absInteger (-6)
6

>>> abs (-6)
6

Used to implement signum for the Num typeclass. This gives 1 for a positive integer, and -1 for a negative integer.

Example

>>> signumInteger 5
1

>>> signum 5
1

Used to implement divMod for the Integral typeclass. This gives a tuple equivalent to

(div x y, mod x y)

Example

>>> divModInteger 10 2
(5,0)

>>> divMod 10 2
(5,0)

Used to implement div for the Integral typeclass. This performs integer division on its two parameters, truncated towards negative infinity.

Example

>>> 10 `divInteger` 2
5

>>> 10 `div` 2

Used to implement mod for the Integral typeclass. This performs the modulo operation, satisfying

((x `div` y) * y) + (x `mod` y) == x

Example

>>> 7 `modInteger` 3
1

>>> 7 `mod` 3
1

Used to implement quotRem for the Integral typeclass. This gives a tuple equivalent to

(quot x y, mod x y)

Example

>>> quotRemInteger 10 2
(5,0)

>>> quotRem 10 2
(5,0)

Used to implement quot for the Integral typeclass. This performs integer division on its two parameters, truncated towards zero.

Example

>>> quotInteger 10 2
5

>>> quot 10 2
5

Used to implement rem for the Integral typeclass. This gives the remainder after integer division of its two parameters, satisfying

((x `quot` y) * y) + (x `rem` y) == x

Example

>>> remInteger 3 2
1

>>> rem 3 2
1

Used to implement (==) for the Eq typeclass. Outputs True if two integers are equal to each other.

Example

>>> 6 `eqInteger` 6
True

>>> 6 == 6
True

Used to implement (/=) for the Eq typeclass. Outputs True if two integers are not equal to each other.

Example

>>> 6 `neqInteger` 7
True

>>> 6 /= 7
True

Used to implement (<=) for the Ord typeclass. Outputs True if the first argument is less than or equal to the second.

Example

>>> 3 `leInteger` 5
True

>>> 3 <= 5
True

Used to implement (>) for the Ord typeclass. Outputs True if the first argument is greater than the second.

Example

>>> 5 `gtInteger` 3
True

>>> 5 > 3
True

Used to implement (<) for the Ord typeclass. Outputs True if the first argument is less than the second.

Example

>>> 3 `ltInteger` 5
True

>>> 3 < 5
True

Used to implement (>=) for the Ord typeclass. Outputs True if the first argument is greater than or equal to the second.

Example

>>> 5 `geInteger` 3
True

>>> 5 >= 3
True

Used to implement compare for the Integral typeclass. This takes two integers, and outputs whether the first is less than, equal to, or greater than the second.

Example

>>> compareInteger 2 10
LT

>>> compare 2 10
LT